As shown in FIGS. 1 and 2, a work piece clamping device of the prior art is composed of a main clamping block 10, a press block 20, a tightening nut 30, and a main bracing rod 40. The main clamping block 10 is of an arcuate construction and is provided in the center thereof with a through hole 11 having at one end thereof an arcuate surface 12. The press block 20 is of an arcuate construction and in contact with the arcuate surface 12. The press block 20 is provided at the center thereof with a through hole 21. The tightening nut 30 is a winged nut. The main bracing rod 40 is a threaded rod which is provided at one end thereof with a stop surface 41. The main bracing rod 40 is jutted out of a locating hole 51 of the workbench top 50 such that the stop surface 41 of the main bracing rod 40 urges the underside of the bench top 50. The main clamping block 10 is engaged with the main bracing rod 40 via the through hole 11. When a work piece 60 is to be secured by the main clamping block 10, the tightening nut 30 must be first loosened so as to unable the main clamping block 10 to move upwards. After the main clamping block 10 is moved upwards, the work piece 60 is located under the main clamping block 10 before the tightening nut 30 is tightened to put the pressure on the press block 20, which in turn puts the pressure on the main clamping block 10 to hold he work piece 60 securely. The main bracing rod 40 is kept perpendicular to the bench top 50 while the work piece 60 is clamped by the main clamping block 10.
When the work piece 60 is fastened or unfastened by the main clamping block 10, the tightening nut 30 must be turned on the main bracing rod 40 back and forth. The is rather time-consuming. In addition, the main bracing rod 40 must be replaced with one which has a greater length so as to facilitate the clamping of a relatively large work piece 60 by the main clamping block 10.